Fast genes and slow clades: comparative rates of molecular evolution in mammals.

Although interest in the rate of molecular evolution and the molecular clock remains high, our knowledge for most groups in these areas is derived largely from a patchwork of studies limited in both their taxon coverage and the number of genes examined. Using a comprehensive molecular data set of 44 genes (18 nDNA, 11 tRNA and 15 additional mtDNA genes) together with a virtually complete and dated phylogeny of extant mammals, I 1) describe differences in the rate of molecular evolution (i.e. substitution rate) within this group in an explicit phylogenetic and quantitative framework and 2) present the first attempt to localize the phylogenetic positions of any rate shifts. Significant rate differences were few and confirmed several long-held trends, including a progressive rate slowdown within hominids and a reduced substitution rate within Cetacea. However, many new patterns were also uncovered, including the mammalian orders being characterized generally by basal rate slowdowns. A link between substitution rate and the size of a clade (which derives from its net speciation rate) is also suggested, with the species-poor major clades ("orders") showing more decreased rates that often extend throughout the entire clade. Significant rate increases were rare, with the rates within (murid) rodents being fast, but not significantly so with respect to other mammals as a whole. Despite clear lineage-specific differences, rates generally change gradually along these lineages, supporting the potential existence of a local molecular clock in mammals. Together, these results will lay the foundation for a broad-scale analysis to establish the correlates and causes of the rate of molecular evolution in mammals.


Introduction
The idea that molecular sequences evolve at a more-or-less constant rate over time (the molecular-clock hypothesis) has underscored research in molecular biology since being proposed for protein sequences by Zuckerkandl and Pauling over 40 years ago Pauling, 1962, 1965). However, it was clear almost from the outset that no single, global clock exists (see Kumar, 2005). One source of variation in the clock stems from inherent differences in rate among the sequences (genes or proteins) themselves as a result of selection on gene function (Hedges and Kumar, 2003) and mutation rate differences across the genome (Ellegren et al. 2003). A second derives from the later realization that the rate within any single sequence can also vary over time or across lineages (Britten, 1986;Drake et al. 1998). This paper focuses on this second, lineage-dependent source of variation.
Differences in the rate of evolution across the major groups of life are dramatic. For instance, HIV has a substitution rate that is about fi ve orders of magnitude faster than that in mammals (Bromham and Penny, 2003) as a result of the notoriously error-prone DNA replication and proofreading machinery in viruses. Moreover, the extremely high substitution rates in viruses (and other pathogens) might also be maintained by selection, given that they provide a mechanism by which to escape the immune response of the hosts.
Even within a more restricted group such as mammals with its similar molecular machinery, rates differences are still apparent. Two long-standing rules of thumb within mammals are that rodents, and murid rodents in particular, demonstrate an elevated substitution rate ("fast rats"), whereas apes and especially humans have a decreased rate (the "hominid slowdown") (see Bromham et al. 1996;Kumar, 2005) compared to other mammal species. Other general trends that have been noted for mammals are that whales have generally slow rates (Martin and Palumbi, 1993); that marsupials have slower rates relative to placentals (Martin and Palumbi, 1993); and that the rate in rodents is faster than that in artiodactyls, which in turn is faster than that in primates (see Bromham et al. 1996). These differences have been ascribed variously to slight differences in the efficiency of DNA proofreading and repair enzymes (Hart and Setlow, 1974;Britten, 1986) and any or all of differences in body size, (genome) generation time, mass-specific metabolic rate, or environmental temperature (see Wu and Li, 1985;Li et al. 1987;Martin and Palumbi, 1993;Bromham et al. 1996;Gillooly et al. 2005).
Although many of the general empirical observations in the preceding paragraph are undoubtedly true, apparent discrepancies also occur, such that even widely-accepted fi ndings might not be true universally. For example, Irwin and Arnason (1991) found exactly the opposite trend for "fast rats" and the "hominid slowdown" in MT-CYB (better known as cytochrome b), with myomorph rodents (as represented by the House Mouse, Mus musculus) having the slowest rate and humans and the African Elephant (Loxodonta africana) having the highest rate among the 10 sequences (representing eight orders) that they examined. Similarly, Eastal (1991) detected a signifi cant decrease in substitution rate in humans relative to Old World monkeys for only one of the 18 genes he examined (ψη−globin).
It remains that investigations characterizing comparative rates of molecular evolution in any single group are often based on a highly limited species sample and/or analyses that employed an, at best, limited phylogenetic framework (e.g. using an unresolved star phylogeny). As such, few broadscale investigations (e.g. Kumar and Subramanian, 2002) have been performed and the observations are usually limited to describing differences in rate between groups, rather than identifying if any rate differences derive from a signifi cant, local rate shift. This study seeks to address this gap in mammals using a comprehensive molecular data set (44 genes comprising 35 427 bp and variously distributed among 2111 species) in concert with a virtually complete dated species-level phylogeny of mammals (Bininda-Emonds et al. 2007) to identify groups with significantly elevated or depressed rates of molecular evolution. Additionally, I present the fi rst attempt to pinpoint the phylogenetic location of any signifi cant changes in rates within mammals. These data will provide an essential foundation to help test between the competing hypotheses (e.g. the metabolic-rate and generation-time hypotheses) of the causal factors infl uencing molecular evolution in mammals.

Materials and Methods
Supertree and gene trees DNA sequence data from 44 genes were mapped on to suitably pruned versions of the dated mammalian supertree of Bininda-Emonds et al. (2007), which with 4510 species is by far the most complete (99.0% of the species listed in Wilson and Reeder (1993)) and resolved species-level phylogeny for this group. For each gene tree, branch lengths representing the average number of substitutions per site were obtained under a maximum likelihood framework in PAUP* 4.0b10 (Swofford, 2002). In all cases, the most appropriate model of evolution for each gene was determined using the AIC criterion in ModelTEST v3.6 (Posada and Crandall, 1998), albeit with a pruned version of the supertree being used instead of the default NJ tree. Likelihood ratio tests indicated that none of the genes evolved according to a strict molecular clock. Further details regarding both the generation of the gene data sets and trees can be found in Bininda-Emonds et al. (2007).
The 44 genes (18 nDNA, 11 tRNA, and 15 other mtDNA; see Table 1) represent a subset of the 68 genes used to estimate divergence times on the supertree, where each gene included representatives from 10 or more of the orders listed in Wilson and Reeder (1993) (with Artiodactyla and Cetacea combined into Cetartiodactyla, and Insectivora split into Afrosoricida and Eulipotyphla) to ensure broad taxon coverage. There is some inherent circularity in this procedure. However, in both cases, the sequence data were fi tted to the same topology under the most appropriate model of evolution, which represents the best estimate of how the data must have evolved. Furthermore, the actual divergence dates were derived from the sequence data of up to 68 genes in combination with 30 fossil calibration points (the latter also representing minimal age constraints), thereby minimizing the circularity for any single gene. A clear benefi t to this circularity is that the correspondence between the nodes on the gene trees and the supertree means that all rates of evolution are made in reference to only to those nodes with robust divergence date estimates (i.e. from fossil Table 1. Genes included for analysis from the data set of Bininda-Emonds et al. (2007) and relevant statistics. "Taxon coverage" refers to the number of orders listed in Wilson and Reeder (1993) (with Artiodactyla and Cetacea combined into Cetartiodactyla, and Insectivora split into Afrosoricida and Eulipotyphla) for which sequences were available. Gene names are standardized according to the Human Genome Nomenclature Committee names (Wain et al. 2002). and/or molecular estimates) and not interpolations from such dates based on relative clade sizes (although the latter could infl uence the former slightly during the correction for any negative branch lengths). Even so, biases might still occur if there has been a concerted acceleration or deceleration of rates across a whole clade for which the root was dated solely using molecular data. In such cases, the rate change could either not be identifi ed or have its location misidentifi ed. All 44 genes were protein-coding except for the 11 tRNAs and the mitochondrial genes MT-RNR1 and MT-RNR2. However, sequences for the nuclear-coding genes APP, BMI1, CREM, and PLCB4 were derived largely or exclusively from untranslated regions fl anking the actual coding sequence. I divide the genes into three more-orless recognizable genomic partitions (nDNA, tRNA, and other mtDNA), largely for convenience. However, reasons exist to suspect rate differences between these partitions. For instance, mtDNA is known to have a higher mutation rate than nDNA, on average, because the mitochondrion is both the source of oxidative phosphorylation in animals (with an increased mutagen production as by-products of metabolic processes) and uses a DNA polymerase-γ with its higher error rate for DNA replication (Bromham and Penny, 2003). Within the mitochondrial genome, tRNAs are distinctly shorter (<100 bps) than the remaining, largely protein-coding genes and are generally held to be relatively conservative evolutionarily.

Gene
Both the dated supertree and the sequence data for the 44 genes are freely available on request and can also be found at http://www.uni-jena. de/~b6biol2/PublicationsMain.html/.

Determining rates of evolution and identifying rate shifts
Because all the nodes in the mammal supertree are dated, it enabled absolute rates of evolution to be calculated for the branches within it rather than the more common and more limited description of relative rates between sister clades in relation to a third group (e.g. as in the relative-rate test of Wu and Li, 1985). For each branch in a given gene tree, the corresponding branch in the mammalian supertree was determined, with the rate of evolution (number of substitutions per site per year) simply being the length of the branch in the gene tree divided by the duration of the equivalent branch in the supertree. The rate of evolution was associated with the descendant (either a node or a species) of the branch in question. Additionally, clade-specifi c rates were determined from the branch-specifi c rates by calculating a series of nested averages, where the rate for a clade was taken to be the arithmetic mean of the rates for all lineages descended from the node subtending that clade. If the descendent lineage was a terminal branch, only the branch-specifi c rate was used. If the descendant lineage was itself a clade, the rate for the lineage was taken to be the arithmetic mean of the cladespecific rate for the descendent clade and the branch-specific rate between the focal and descendant clades.
In attempting to identify fast-or slow-evolving branches or clades, the assumption is that any global increase or decrease in the evolutionary rate will be mirrored consistently across all genes for a given branch or clade. When comparisons were made across all genes, two procedures were used to compensate for rates of molecular evolution being gene-specifi c and therefore often differing greatly. First, all individual absolute rates were log-transformed (base e) to correct for any large differences in gene-specifi c rates that would bias parametric (paired) statistical tests. In so doing, a correction needs to be made for rates of magnitude zero (for which the logarithm is undefi ned), which involved adding the exponent of a given rate to its raw value. Thus, for example, the corrected value for a rate of 1.68 × 10 -9 was ln(1.68 × 10 -9 + 10 -9 ).
When the rate to be tested itself was zero, the exponent from the rate it was being compared to was added instead. Second, all comparisons were paired, such that the tested (ln-transformed) rate for a given gene was only compared to some reference (ln-transformed) rate for the same gene. The use of pairwise comparisons also accounts for any gene-specifi c differences, such as differences in base composition or GC content, which would otherwise necessitate the removal of the heterogeneous genes from the analysis (e.g. Kumar and Subramanian, 2002), a procedure that has been argued to be unjustifi ed (Ellegren et al. 2003). Note that these corrections, and the second in particular, were performed without regard to the genomic partition to which a gene belong (i.e. nDNA, tRNA, or other mtDNA).
Together, these two corrections ensure that the scale of the difference between the rates being compared and not their magnitude is of primary importance. For both branch-and clade-specifi c rate investigations, both paired parametric (Student's t-test) and nonparametric (Fisher's sign test) two-tailed statistical analyses were used, with a nominal α = 0.05. Corrections for multiple comparisons employed a sequential Bonferroni technique (Rice, 1989).
Essentially, the branch-specifi c analyses attempt to identify localized rate changes, perhaps associated with a major adaptive event (e.g. an adaptive radiation or ecological transition) or a severe environmental disturbance likewise engendering a rapid adaptive response. By contrast, the clade-specifi c analyses attempt to identify entire clades with an altered evolutionary rate, even if no single branch within or leading to that clade displays a signifi cant rate shift. To identify fast-and slow-evolving branches or clades, the respective tested rates were compared to one of two reference rates for a given gene: 1) that representing the average rate across mammals (= the clade-specifi c rate of the root node of the gene tree) or 2) that representing an ancestral node on the supertree that was no more than three intervening branches removed from the target node. The former set of "rate-outlier" analyses attempt to identify branches or clades with substitution rates that differ significantly from the global mammalian average, whereas the latter "rate-shift analyses" attempt to pinpoint where any signifi cant, local changes in rate have occurred. For instance, the fact that a number of closely neighbouring branches or clades are all identifi ed as (global) rate outliers could result from a single rate shift in the oldest branch or clade, with the new rate being inherited by the descendent lineages. Moreover, the rate-shift analyses can also identify branches or clades with rates that differ signifi cantly from the local value, even though they might not differ signifi cantly from the global mammalian average, In both the rate-outlier and rate-shift analyses, fast-or slow evolving branches or clades were defined as those where either the average (arithmetic mean) paired difference over all genes compared to the reference node differed significantly from zero (paired t-test) or the proportion of positive comparisons differed significantly from 0.5 (paired sign test). For the rate-shift analyses, the ancestral reference node was taken to be the one yielding the greatest number of paired comparisons or was the closest to the target node in the case of a tie. For presentation purposes, the proportion of values underlying the sign test is presented as (n + -n -)/(n + + n -), such that proportions of 1 and -1 indicate all positive and all negative comparisons, respectively. The methods and tests described in this section (apart from any corrections for multiple comparisons) have all been implemented in the Perl script moleRat v1.0, which is freely available at http://www.uni-jena.de/~b6biol2/ ProgramsMain.html/. In this study, the default values for the program were used, including the option to ignore all branches in the gene trees with a length of less than 0.0001 substitutions per site per unit time.

Gene-specifi c rates of evolution
The average absolute rates of evolution for the 44 genes ( Figure 1) are generally on an order of magnitude of either 10 -8 or 10 -9 substitutions per site per year and range between 4.92 × 10 -10 (CREM) and 4.95 × 10 -8 (MT-TQ), a difference of nearly two full orders of magnitude. These values agree broadly with those published previously, although they are signifi cantly higher than the mammalian average of 2.2 × 10 -9 calculated across 5669 genes by Kumar and Subramanian (2002) (one-sample Student's t = 5.70, df = 43, p < 0.0001). Rates for genes comprising primarily untranslated regions of coding genes were distributed throughout the nuclear genes, including the two slowest rates (APP and CREM) and one of the fastest (PLCB4).
An ANOVA revealed a significant difference in rate between the genomic partitions (F 2,41 = 4.883, p = 0.0125), with Fisher's PSLD test showing that nDNA is evolving significantly slower than tRNA (by 2.6×; p = 0.0033). In fact, despite being widely perceived as being conserved evolutionarily, tRNA genes exhibited the fastest rates of all partitions on average, although they were not significantly different from those of the remaining mtDNA genes (1.6 × faster; p = 0.0783), which, in turn, were not significantly different from those of the nDNA genes (1.6 × faster; p = 0.1783). However, these observations do not exclude the possibility that the unexpectedly higher rates in tRNA genes derive primarily from substitutions concentrated in hypervariable regions or are due to stochastic variation arising from the extremely short sequence lengths (<100 bp). In the latter case, however, there is no reason why any stochastic variation would cause all tRNA genes to show such a relative uniformity in rate, or at least not one any appreciably greater than for nDNA and other mtDNA genes.

Branch-specifi c rates of evolution
Rate estimates were available for 1246 of the internal and 2086 of the terminal (species) branches of the supertree, or about half (50.3%) of all 6618 branches. Across the entire tree, slowdowns in outlier rates are more common ( Figure 2): average paired difference ± SE = -0.571 ± 0.018 (n + = 815; n -= 2517; n 0 = 0) and average proportion ± SE = -0.378 ± 0.013 (n + = 773; n -= 2270; n 0 = 289). Only six branches exhibit a rate that is signifi cantly faster than the mammalian average (summarized in Table 2). All six subtend clades, most of which characterized major lineages comprising two or more orders (the two exceptions being the branches leading to Bovidae and Hystricomorpha + Myomorpha). Many more branches were indicated to have significantly slow rates of evolution, including the branch leading to Monotremata and most branches within this clade, the branches leading to each of the great ape species except the Orangutan Pongo pygmaeus, two major clades within mysticete whales as well as numerous individual cetacean species, the branch leading to Perissodactlya and numerous branches within this order, and several branches leading to or within Afrotheria and Xenarthra (Table 2). In fact, the majority of the slow branches identifi ed (55 of 68 for the paired t-test; 52 of 70 for the paired sign test) were terminal ones leading to individual species, indicating that the potential confounding of the mutation and substitution rates (sensu Ho and Larson 2006) was not a problem here.
Few local shifts in branch-specific rates were detected among the 3243 branches with a suitable reference branch (summarized in Tables 3  and 4). Again, rate slowdowns were more common across the tree, although not to the same degree as for the outlier rates ( Figure 3): average paired difference ± SE = -0.150 ± 0.019 (n + = 1419; n -= 1824; n 0 = 0) and average proportion ± SE = -0.070 ± 0.014 (n + = 1210; n -= 1530; n 0 = 503). Rate-shift analyses confirmed that all fast outlier branches also represent significant local rate shifts. Three additional local speedups were also indicated in the branches leading to Cetartiodactyla + Perissodactyla, Delphinidae + Phocoenidae within Cetacea, and Microchiroptera. Significant local slowdowns were concentrated in Cetacea, but also occurred along the branches 1.0 x 10 -9 leading to Boreoeutheria, Tubulidentata, Xenarthra, and, most interestingly, the rodent families Dipododae + Muridae. These results did not change appreciably when the rate-shift analyses were constrained such that the ancestral, reference branch was the immediate ancestor of the target branch (compare Tables 3 and 4).

Clade-specifi c rates of evolution
Clade-specifi c rate estimates were present for 1282 of the 2108 nodes (60.8%) on the mammal supertree. As for the branch-specifi c rates, the overall trend is for a predominance of rate slowdowns in the outlier rates ( Figure   n 0 = 1) and the average proportion ± SE = -0.323 ± 0.021 (n + = 327; n -= 834; n 0 = 120). Clades identifi ed as signifi cant rate outliers (Table 5) generally refl ect the results of the branch-specifi c analyses. Important slow clades include Monotremata and Tachyglossidae, the clade Cetartiodactyla + Perissodactyla and numerous clades within each order, squirrel-like rodents (Sciuromorpha), the hominoid clades Homo + Pan and Pan, and several major clades in Carnivora and in the superorders Afrotheria and Xenarthra. The traditional orders seem to be disproportionately characterized as being significantly slow, with examples including Afrosoricida, Carnivora, Chiroptera, Eulipotyphla (albeit excluding Soleonodontidae), Lagomorpha, Marsupialia, Monotremata, Perissodactyla, and Xenarthra. The only fast clades compared to mammals as a whole were Theria (= Eutheria + Marsupialia) and Eutheria. The latter observations are underscored more strongly by the restricted view in Figure 5 that reveals that nearly all the major mammalian lineages -generally, the orders, with the addition of the branch-specifi c outlier rate for the monotypic Tubulidentata (= Orycteropus afer) -show slower rates, and usually signifi cantly slower rates, than do mammals as a whole. The only "fast" clades are Eutheria, Rodentia, and, as indicated by the paired t-test only, Eulipotyphla. Only the increased rate for Eutheria was significantly increased (average paired difference = 0.924) and, interestingly, mirrored the magnitude of the signifi cantly decreased rates characterizing its sister clade, Marsupialia (-1.060), nearly exactly in magnitude.
The rate-shift analyses confi rm that most fast and slow rate-outlier clades also represent instances of signifi cant local rate changes ( Figure 6; Tables 6 and 7). Signifi cant local increases were also found for Boreoeutheria, Rodentia, the clade of sea lions in Carnivora, a major clade within Cetacea, and Cetartiodactyla as a whole. Important local slowdowns include the clades of Boreoeutheria + Xenarthra (compared to the fast Eutheria) and Myomorpha + Hystricomorpha (compared to the fast Rodentia); both instances apparently derive from the fast branch-specifi c rates associated with each clade. Finally, the hominoid clade of Gorilla + Homo + Pan as a whole, but no clades within it, was inferred to have undergone a local slowdown. The more restrictive rate-shift analyses ( they identifi ed only a subset of the clades inferred to have undergone a signifi cant shift in the cladespecifi c rate of evolution. Altogether, many of the groups displaying rate shifts represent classic mammalian orders or major groupings thereof, suggesting a slowdown in the rate of molecular evolution following their establishment and initial diversifi cation. Otherwise, rate-shifts in cladespecifi c rates across the tree showed the same tendency towards local slowdowns as seen in the other analyses: average paired difference ± SE = -0.155 ± 0.017 (n + = 558; n -= 703; n 0 = 2) and the average proportion ± SE = -0.055 ± 0.022 (n + = 491; n -= 599; n 0 = 171).

Discussion
Overall, the results indicate that the rate of molecular evolution across many genes considered simultaneously is relatively homogeneous among mammals, with comparatively few significant outlier rates or rate shifts being detected for both branch-and clade-specifi c rates. A similar conclusion was reached by Kumar and Subramanian (2002), albeit with fewer taxa (326) but many more genes (5669). Together, these fi ndings could be taken as evidence supporting a local (but not global) molecular clock (at least for mammals), an idea that at least implicitly underlies many of the relaxed molecular clock methods currently being used to derive divergence times from molecular data (for recent reviews, see Renner, 2005;Welch and Bromham, 2005). However, these fi ndings also do not exclude the possibility that rates are changing substantially and frequently, but only among selected genes in selected lineages (e.g. Smith and Eyre-Walker, 2003). Such changes, naturally, point to a gene-specifi c, selection-driven alteration in rate, rather than to a global change in the rate of molecular evolution between lineages associated with differences in any or all of body size, (genome) generation time, mass-specific metabolic rate, or environmental temperature. The few signifi cant differences in rate observed largely corroborate the previous general conclusions of other workers. For instance, as noted by Martin and Palumbi (1993), whales were confi rmed as generally being characterized by a slow substitution rate, whether for entire clades or numerous individual species. Several shifts to even slower rates of evolution within Cetacea were also observed. Similarly, there is good support for progressive local rate decreases within hominids across a large number of genes (contra Eastal, 1991), thereby supporting the existence of the "hominid slowdown" (see Bromham et al. 1996;Kumar and Hedges, 1998). Marsupials were also shown to have a slower rate compared to placental mammals (Martin and Palumbi, 1993) and, in fact, both taxa differed signifi cantly from the overall mammalian average in their clade-specifi c rates (slower and faster, respectively).
The broad taxon sampling in this study also allowed the identifi cation of several apparently novel trends, including general rate slowdowns in monotremes, perissodactyls, and various afrotherian taxa. Moreover, there appears to be a tendency for rate slowdowns to be concentrated basally   among the orders or major mammalian lineages; apart from Cetacea and hominids, few rate slowdowns were associated with species or more terminal clades in the tree. The more depauperate major lineages (e.g. Afrotheria, Perissodactyla or Xenarthra) also seem to be characterized by more systemic slowdowns occurring throughout the clade, suggesting a possible link between the rate of molecular evolution and the net rate of speciation. This supposition is supported by the observation of weak, but signifi cant relationships between the ln-transformed sizes of the orders in Figure 5 (which yield non-nested and therefore reasonably phylogenetically independent data points) and their clade-specifi c rates of evolution as given by either the parametric paired difference (p = 0.0012, df = 19, R 2 = 0.449) or the non-parametric proportion of positive values (p = 0.0285; df = 19, R 2 = 0.240).
For the former set of analyses at least, this relationship still holds even when the Rodentia are excluded as a potential outlier. Although the relationship here deals with molecular rates and not total amount of molecular change, it still agrees with the predictions of Pagel et al. (2006) and so might support their arguments for an increased role for punctuational effects in speciation. It cannot be excluded, however, that the signifi cant association derives at least in part from the known nodedensity artifact where the degree of molecular change is apparently increased in those parts of the tree with denser taxon sampling (Fitch and Beintema, 1990;Webster et al. 2003), although the use of maximum likelihood to derive the gene trees under the inferred optimal model of evolution should mitigate any negative effects ). An unexpected result given the widespread acceptance of the "fast-rats" hypothesis was that few signifi cantly increased substitution rates were found at any level within rodents. At best, only two signifi cant rate increases were observed, neither of which were associated directly with murids: a fast outlier rate for the branch leading to Hystricomorpha + Myomorpha (the latter of which does contain Muridae, however) and a clade-specifi c rate shift for rodents as a whole. However, rodents did possess among the fastest rates of all the orders examined and are generally characterized by increased outlier rates (e.g. see Figure 5), and for both branches and clades, just not signifi cantly increased ones. Previous evidence for an elevated rate of evolution for (murid) rodents also derives largely from specifi c, pairwise comparisons with other, slower groups (such as primates), thereby accentuating lineage-specifi c differences and not the more global and local perspectives examined here. Interestingly, Kumar and Subramanian (2002) also show that rate differences within each of primates and rodents are of similar magnitudes to those between the two taxa, indicating that that apparent rate increase in rodents may have been overstated or is dependent on the species being investigated.
Thus, the general lack of any signifi cant rate shifts within rodents appears to indicate a real lack of any dramatic local changes in the substitution rate within  Clade-specifi c rates of evolution for selected clades of mammals (outlier rates). Rates were evaluated with either (a) a t-test or (b) a sign test (red = signifi cantly fast / slow at a nominal alpha of 0.05; green = not signifi cant; blue = insuffi cient sample size for testing). The dashed line indicates the average value across mammals. In (a), values represent average paired difference (± SE) between the target clade and the gene-specifi c rate for all relevant genes. The rates for the clades labeled "Macroscelididae" and "Scandentia" actually represent those for Macroscelididae without Rhynchocyon and Tupaiinae, respectively. the group. However, it cannot be excluded that the result is a partial artifact of the high substitution rates in rodents causing the divergence time estimates in this clade being too old (see Steppan et al. 2004), thereby causing the inferred substitution rates to be underestimated. Indeed, the divergence time in the supertree for the split between the murid genera Mus and Rattus of 30.3 million years ago (mya) is over three times that advocated by Steppan et al. (2004) based on paleontological evidence (8.8 -10.3 mya). This problem would not affect pairwise comparisons between rodents and another group, where divergence time would be factored out because both lineages would be equally old. Interestingly, the observations of Irwin and Arnason (1991) with respect to the "inverted" relative substitution rates in MT-CYB were upheld partly here. In particular, the three hominoid primates Homo sapiens, Pan paniscus, and Pan troglodytes did indeed all possess higher rates of evolution for this gene (8.16 × 10 -9 , 6.07 × 10 -9 , and 9.88 × 10 -9 substitutions per site per year, respectively) than did the rodents Mus musculus and Rattus novegicus (4.78 × 10 -9 and 5.23 × 10 -9 , respectively). The latter pair of rates also fell below the overall rate for MT-CYB of 6.37 × 10 -9 substitutions per site per year. Loxodonta africana, however, displayed the slowest rate for this gene among the relevant species at 3.85 × 10 -9 substitutions per site per year (contra Irwin et al. 1991).
Finally, some evidence of non-independent rate shifts exists. For instance, the shifts to a slower rates for the branches leading to either Myomorpha or Muridae + Dipodidae derive from these branches being compared to the rate for the branch leading to Hystricomorpha + Myomorpha, a significantly fast branch. So, although the rate slowdown is perhaps unexpected here, it would only be in a global sense; these results otherwise seem to reflect local events accurately. More importantly, there does not seem to be much evidence of the truly artifactual "trickle-down effect" (sensu Moore et al. 2004), whereby a large outlier rate for a clade is passed down the tree to its parent clade. Instances of congruent significant outlier rates among linked clades are present in Table 5 (e.g. within Carnivora, Cetacea, or Perissodactyla), but the rate for the parental clade is often more significant than that for the daughter clade, indicating an additive effect of the sister clades. Under a trickle-down scenario, the effect would be expected instead to dissipate progressively going up the tree.

Conclusions
The comparative paucity of signifi cant rate differences observed in this study cannot be taken to mean that lineage-specifi c differences are largely absent among mammals, simply that few differences exist with respect to either the overall mammalian average (outlier-rate analyses) or from a local reference point (rate-shifts analyses). Systematic, signifi cant differences in rate could  still exist between specific lineages, such as between rodents and primates for example (see also Figure 5), and perhaps also restricted to specific genes (e.g. Smith and Eyre-Walker 2003). This fact is underscored by the large differences in the rate of evolution that are apparent here. Among those values for average paired differences in rate that could be tested signifi cantly (i.e. paired n >1), the fastest branch was that leading to the node joining the bat genera Molossus and Promops (3.47), whereas the slowest was that leading to the Black Mastiff Bat, Molossus ater (-4.91), a species within the former clade. The respective values for clade-specific rates are less extreme, but still dramatic, with the fastest and slowest clades being a clade of fi ve Macaca species (2.51) and the species pair of Didelphis aurita and Didelphis marsupialis (-2.93), respectively. Differences in rate within any single gene are even more dramatic, with the difference between the slowest and fastest branch-specific rate for a given gene ranging between 114× (TYR) and 1.12 × 10 9 × (MT-TF) (results not shown).
Despite concerted effort, the reasons underlying any global lineage-specifi c differences remain unclear, with explanations invoking or refuting any or all of differences in cellular DNA proofreading and repair mechanisms, body size, mass-specifi c metabolic rate, and/or (genomic) generation time (for a recent review, see Kumar and Hedges, 1998). The current data set, together with a database containing relevant trait data for a large number of mammal species (http://www. biodiversitydata.group.cam.ac.uk/pantheria/pantheria. html), will allow for a more broadly-based, phylogenetic analysis than has been possible before now, thereby providing key insights into the correlates and causes of global differences in the rate of molecular evolution.